The invention relates to a method for simulating the movement or distribution of particles in a medium under the influence of a changing phase interface between two neighboring phases in said medium and to a computer program product comprising software code to perform said simulation. A changing interface in the context of the invention means an interface which moves at least partially in the course of time.
The properties of most semiconductor devices, such as MOSFETs, are determined by the spatial arrangement of so-called dopant or (impurity) atoms, such as e.g. boron or arsenic atoms. In the absence of dopant atoms, the conductivity of the semiconductor is quite low. Regions with a high concentration of so called donor atoms (such as arsenic or phosphorus) are called n-type regions, because in such regions the concentration of negatively charged free electrons in the semiconductor is increased. Regions with a high concentration of so called acceptor atoms (such as boron or indium) are called p-type regions, because in such regions the concentration of positively charged free holes is increased. A positively charged hole can be understood as a missing electron.
In the fabrication process of semiconductor devices, such as transistors, one of the main tasks is to achieve a certain spatial distribution of dopant atoms in the device. Usually, at the beginning of a fabrication process, one starts with a semiconductor wafer with a uniform dopant concentration, and at the end of the fabrication process, one has different doping concentrations in different regions of the device.
In state-of-the art semiconductor technology, the following method is frequently used to fabricate regions with different concentration of dopant atoms:
In a first step, dopant atoms are implanted into the semiconductor crystal by so-called ‘ion implantation’, i.e. by shooting dopant atoms at the semiconductor with high energy. Using different ion acceleration energies, one can adjust the average depth from the semiconductor surface, at which the ions come at rest in the semiconductor. By using masks one can achieve that the implanted ions will enter the semiconductor only at desired regions.
In a second so-called annealing step, the semiconductor wafer is subject to a high temperature treatment, e.g. treating the wafer 10 seconds at 1000° C., or 1 hour at 70° C. This is necessary to heal crystal damage which is caused by ion implantation, and to electrically activate the dopant atoms, i.e. to put them into semiconductor lattice sites, which requires some thermal energy. The temperatures needed to heal the crystal damage and to activate the dopant atoms are so high, that the dopant atoms diffuse in the semiconductor crystal. Therefore, not only the crystal damage and the activation of the dopant atoms changes, but also the spatial distribution of dopant atoms may change during an annealing step.
Fabrication processes of semiconductor devices can be modeled with the help of computer simulations which are based on physical models, so called process simulations. A main goal of process simulations is to calculate accurately the distribution and the electrical activation of dopant atoms in the completed semiconductor device. This allows to compute the electrical characteristics of the devices and to study the effect of changes in the fabrication process on the device characteristics. Such process simulations are done by most of the manufacturers of integrated circuits. An example for such a process simulation can be found in the European Patent Application EP 0 864 991.
The implantation of a high dose of dopant atoms causes a lot of crystal damage to the exposed semiconductor surface. The reason is, that the incident high energy ions can collide with the semiconductor atoms, before they eventually come to rest, and kick semiconductor atoms out of their ideal lattice site. If the implantation dose is so high, that most of the semiconductor atoms in a certain volume of the silicon are kicked to some other position in the crystal, then the crystalline order of this volume is finally completely lost, and the region is considered to be amorphous. Those parts of the semiconductor wafer, which are not exposed to the ion bombardment or which are too far from the surface to be reached by the implanted ions, remain crystalline.
Upon high temperature treatment, an amorphized region of semiconductor will recrystallize. If the amorphous region is neighboring a crystalline region, the crystallization process usually occurs in the form of a solid phase epitaxial (SPE) regrowth (see e.g. G. L. Olson and J. A. Roth, ‘Kinetics of Solid Phase Crystallization in Amorphous Silicon’, Mat. Sci. Rep. Vol 3, Nr. 1, June 1988, pp. 1-78).
In SPE regrowth, the amorphous material crystallizes along the interface between crystalline and amorphous material. The crystalline region acts as a seed for crystallization. Starting at the interface between the amorphous and the crystalline phase, the atoms of the amorphous part are rearranged in such a way, that they extend the crystalline microstructure of the crystalline part. By this mechanism, the crystalline region becomes larger and the amorphous region becomes smaller. The interface between amorphous and crystalline structure moves towards the amorphous part of the material, until eventually the complete amorphous part is recrystallized.
The distribution of dopant atoms in the semiconductor can change in the course of time, e.g. during the SPE regrowth, either by diffusion, or by some force pushing the atoms in a certain direction. In particular, during SPE regrowth, dopant atoms, which are in the amorphous part of the device before the SPE, can be pushed in the direction of the recrystallization front. The driving force for this dopant-pushing is, that dopant atoms are in an energetically more favorable state in the amorphous region of the semiconductor. Near the crystallization front of the SPE, such dopant atoms prefer to stay at the amorphous side of the amorphous-crystalline interface, rather than being incorporated into the crystal structure of the crystalline part. In this situation, in average, each dopant atom which is originally situated in the amorphous part of the device may be shifted a certain distance until it is eventually built into the crystalline material.
This dopant redistribution during SPE can have a significant impact on the final distribution and electrical activation of dopants in semiconductor devices. Therefore, it has a significant impact on the electrical characteristics of such devices.
Until now there is no process simulation available with which it is possible to determine accurately the movement and redistribution of the dopants during annealing steps in a medium having two different phases, particularly during SPE regrowth. As annealing is very essential to the production of semiconductor devices, it is of a great interest to determine the movement or distribution of the dopants by means of a computer simulation.